The most luminous blue quasars at 3.0<z<3.3 - III. LBT spectra and accretion parameters

We present the analysis of the rest frame ultraviolet and optical spectra of 30 bright blue quasars at $z\sim3$, selected to examine the suitability of AGN as cosmological probes. In our previous works, we found an unexpectedly high fraction ($\approx 25 \%$) of X-ray weak quasars in the sample. The latter sources also display a flatter UV continuum and a broader and fainter CIV profile in the archival UV data with respect to their X-ray normal counterparts. Here we present new observations with the LBT in both the $zJ$ (rest-frame $\simeq$2300-3100 $\rm \mathring{A}$) and the $K_S$ ($\simeq$4750-5350 $\rm \mathring{A}$) bands. We estimated black hole masses ($M_{\rm BH}$) and Eddington ratios ($\lambda_{\rm Edd}$) from the from the H$\beta$ and MgII emission lines, finding that our $z\sim3$ quasars are on average highly accreting ($\langle \lambda_{\rm Edd} \rangle\simeq 1.2$ and $\langle M_{\rm BH} \rangle\simeq 10^{9.7}M_\odot$), with no difference in $\lambda_{\rm Edd}$ or $M_{\rm BH}$ between X-ray weak and X-ray normal quasars. From the $zJ$ spectra, we derive flux and equivalent width of MgII and FeII, finding that X-ray weak quasars display higher FeII/MgII ratios with respect to typical quasars. FeII/MgII ratios of X-ray normal quasars are instead consistent with other estimates up to $z\simeq6.5$, corroborating the idea of already chemically mature BLRs at early cosmic time. From the $K_S$ spectra, we find that all the X-ray weak quasars present generally weaker [OIII] emission (EW<10 $\rm \mathring{A}$) than the normal ones. The sample as a whole, however, abides by the known X-ray/[OIII] luminosity correlation, hence the different [OIII] properties are likely due to an intrinsically weaker [OIII] emission in X-ray weak objects, associated to the shape of the spectral energy distribution. We interpret these results in the framework of accretion-disc winds.